The side of an equilateral triangle is increa | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $a$ be the side of the equilateral triangle and $A$ be its area.The area of an equilateral triangle is given by $A = \frac{\sqrt{3}}{4} a^2$.D

Vedclass · Accepted Answer

$20 \sqrt{3} 	ext{ cm}^2/	ext{s}$

Vedclass · Answer

(C) Let $a$ be the side of the equilateral triangle and $A$ be its area.The area of an equilateral triangle is given by $A = \frac{\sqrt{3}}{4} a^2$.Differentiating both sides with respect to time $t$,we get:$\frac{dA}{dt} = \frac{\sqrt{3}}{4} 	imes 2a 	imes \frac{da}{dt} = \frac{\sqrt{3}}{2} a \frac{da}{dt}$.Given that $\frac{da}{dt} = 2 	ext{ cm/s}$ and $a = 20 	ext{ cm}$.Substituting these values into the equation:$\frac{dA}{dt} = \frac{\sqrt{3}}{2} 	imes 20 	imes 2 = 20 \sqrt{3} 	ext{ cm}^2/	ext{s}$.Thus,the rate at which the area is increasing is $20 \sqrt{3} 	ext{ cm}^2/	ext{s}$.

The side of an equilateral triangle is increasing at the rate of $2 \text{ cm/s}$. Find the rate at which the area is increasing when the side of the triangle is $20 \text{ cm}$.

Similar Questions

$A$ car starts from a point $P$ at time $t=0$ seconds and stops at point $Q$. The distance $x$,in metres,covered by it in $t$ seconds is given by $x=t^{2}(2-\frac{t}{3})$. Find the time taken by it to reach $Q$ and also find the distance between $P$ and $Q$.

$A$ particle is moving in a straight line. At time $t$,the distance of the particle from its starting point is given by $x = t^3 - 6t^2 + t$. Its acceleration will be zero at

The diagonal of a square is changing at the rate of $0.5 \text{ cm/sec}$. Then the rate of change of area when the area is $400 \text{ cm}^2$ is equal to

If $x$ and $y$ are sides of two squares such that $y = x - x^2$,then the rate of change of area of the second square with respect to that of the first square is

If the displacement of a particle at a point is given by $s = 3t^{2} - 12t + 14$, then the displacement of the particle when its velocity becomes zero is (in $\text{ units}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module